Abstract

A new method for measuring atmospheric refraction angles is presented, with in-orbit measurements demonstrating a precision of ±0.02
arcsec (±0.1μrad). Key advantages of the method are the following: (1) Simultaneous observation of two celestial points during occultation (i.e., top and bottom edges of the solar image) eliminates error from instrument attitude uncertainty. (2) The refraction angle is primarily a normalized difference measurement, causing only scale error, not absolute error. (3) A large number of detector pixels are used in the edge location by fitting to a known edge shape. The resulting refraction angle measurements allow temperature sounding up to the lower mesosphere.

Figures (13)

Refraction geometry. The red line depicts the path of light through the Earth’s limb to the sensor, shown as a large solid dot. The refraction angle, α, is the change in direction of the ray from when it enters the atmosphere to where it is received at the sensor. This is approximately the difference between the geometric angle and the observed impact angle at the satellite (θG minus θO). The radius at the impact tangent point, the point of closest approach for the observed ray at angle θO, is called the impact radius, rO. The altitude above the surface for the same point is called the impact altitude. The true refracted point of minimum perigee is labeled rT.

Refracted and unrefracted images of the setting Sun at five different snapshot times as they would appear from a low-Earth orbit. The chosen elapsed time between image 2 and image 5 is the time, Δt, required for the straight ray to the top edge of the Sun to move one unrefracted solar extent relative to the constant geopotential height horizon. Δt=t5−t2. Note that αT(t5)=αB(t5−Δt). It can be shown that αB(t)=Eo−E(t)+αB(t−Δt), where Eo is the unrefracted vertical extent and E(t) is the refracted (observed) vertical extent (note Eo=E(t) above the atmosphere).

Fine Tracking State (illustrative—not to scale). The Sun image is kept within the FPA by the spacecraft. The science FOV is fixed relative to the Sun sensor FOV. Tracking the solar edges locates the science FOV relative to the solar image and provides the image extent used for refraction angle measurements. Center sums are used to measure atmospheric transmission, which is incorporated into the edge intensity model.

Empirical Top Edge Model. The black line is the Boltzmann function model for top edge. The red are the 560,000 individual data points from the top edge and the many events used to determine the parameters for the Boltzmann function.

Empirical Bottom Edge Model. The black line is the Boltzmann function model for bottom edge. The red are the 560,000 individual data points from the bottom edge and the many events used to determine the parameters for the Boltzmann function.

Comparison of temperature profiles for two events, late fall and summer of 2008. Black is the temperature retrieval from the SOFIE 4.3μm radiometer channel. The red is from the refraction angle analysis. The green, added for comparison, is from the NCEP product, extended above 50km with MSIS.

Statistical comparison of 31 temperature profiles retrieved from refraction angle versus those retrieved from CO2 transmission. Temperature and pressure from CO2 transmission is used to simulate a refraction angle upper boundary. The three comparisons are for three different upper boundary merge windows, which are roughly 15km high with bottom starting at approximately 55, 60, and 65km. Also plotted is the standard deviation about the mean difference. (The bias between 40 and 50km is a known error in the SOFIE temperature retrieval using the 4.3μmCO2 transmission and will be corrected in a future data release.)